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CS461/ECE422 Spring 2012 Commercial Symmetric systems DES AES Modes of block and stream ciphers 1/31/12 Nikita Borisov — UIUC 2 Chapters 2 and 20 from text. AES Standard issued as FIPS PUB 197 http://csrc.nist.gov/publications/fips/fips197/fips- 197.pdf Handbook of Applied Cryptography, Menezes, van Oorschot, Vanstone Chapter 7 http://www.cacr.math.uwaterloo.ca/hac/ 1/31/12 Nikita Borisov — UIUC 3 E encipherment function Ek(b) encipherment of message b with key k In what follows, m = b1b2 …, each bi of fixed length Block cipher Ek(m) = Ek(b1)Ek(b2) … Stream cipher k = k1k2 … Ek(m) = Ek1(b1)Ek2(b2) … If k1k2 … repeats itself, cipher is periodic and the length of its period is one cycle of k1k2 … 1/31/12 Nikita Borisov — UIUC 4 Vigenère cipher |bi| = 1 character, k = k1k2 … where |ki| = 1 character Each bi enciphered using ki mod length(k) Stream cipher DES |bi| = 64 bits, |k| = 56 bits Each bi enciphered separately using k Block cipher 1/31/12 Nikita Borisov — UIUC 5 Key desirable property of an encryption algorithm Where a change of one input or key bit results in changing approx half of the output bits If the change were small, this might provide a way to reduce the size of the key space to be searched DES exhibits strong avalanche 1/31/12 Nikita Borisov — UIUC 7 A block cipher: encrypts blocks of 64 bits using a 56 bit key outputs 64 bits of ciphertext A product cipher basic unit is the bit performs both substitution (S-box) and transposition (permutation) (P-box) on the bits Cipher consists of 16 rounds (iterations) each with a round key generated from the usersupplied key Slide #9-8 1/31/12 Nikita Borisov — UIUC 8 Structured to enable use of same S-box and P-box for encryption and decryption Change only key schedule Major feature is key division and swapping L(i) = R(i-1) R(i) = L(i-1) xor f(K(i), R(i-1)) 1/31/12 Nikita Borisov — UIUC 9 1/31/12 Nikita Borisov — UIUC 10 1/31/12 Nikita Borisov — UIUC 11 input IP L0 R0 f K1 R1 = L0 f(R0 , K1) L1 = R0 L16 = R15 R16 = L15 - f(R15, K16) Š1 IP output Slide #9-13 1/31/12 Nikita Borisov — UIUC 13 R iŠ1 (32 bits) Ki (48 bits) E R iŠ1 (48 bits) S1 S2 S3 S4 6 bits into each S5 S6 S7 S8 4 bits out of each P 32 bits Slide #9-14 1/31/12 Nikita Borisov — UIUC 14 Key non-linear element to DES security have eight S-boxes which map 6 to 4 bits outer bits 1 & 6 (rowbits) select one rows inner bits 2-5 (colbits) select column result is 8 lots of 4 bits, or 32 bits row selection depends on both data & key feature known as autoclaving (autokeying) example: S(18 09 12 3d 11 17 38 39) = 5fd25e03 1/31/12 Nikita Borisov — UIUC 15 decrypt must unwind steps of data computation with Feistel design, do encryption steps again using subkeys in reverse order (SK16 … SK1) note that IP undoes final FP step of encryption 1st round with SK16 undoes 16th encrypt round …. 16th round with SK1 undoes 1st encrypt round then final FP undoes initial encryption IP thus recovering original data value 1/31/12 Nikita Borisov — UIUC 16 Considered too weak Diffie, Hellman said in a few years technology would allow DES to be broken in days ▪ Design using 1999 technology published Design decisions not public ▪ NSA controlled process ▪ Some of the design decisions underlying the S-Boxes are unknown ▪ S-boxes may have backdoors ▪ Key size reduced from 112 bits in original Lucifer design to 56 bits 1/31/12 Nikita Borisov — UIUC 17 4 weak keys They are their own inverses i.e. DESk(m) = c DESk (c) = m All 0’s. All 1’s. First half 1’s second half 0’s. Visa versa. 12 semi-weak keys Each has another semi-weak key as inverse i.e. DESk1(m) = c DESk2 (c) = m Possibly weak keys Result in same subkeys being used in multiple rounds Complementation property DESk(m) = c DESk (m ) = c 1/31/12 Nikita Borisov — UIUC 18 What do you need? How many steps should it take? How can you do better? 1/31/12 Nikita Borisov — UIUC 19 Double encryption not generally used Meet-in-the-middle attack C = Ek2(Ek1(P)) Modifies brute force to require only 2n+1 steps instead of 22n Encrypt-Decrypt-Encrypt Mode (2 or 3 keys: k, k ) c = DESk(DESk –1(DESk’’(m))) Also called Triple DES or 3DES when used with 3 keys 168 bits of key, but effective key length of 112 due to meet-in-the middle Not yet practical to break but AES much faster Encrypt-Encrypt-Encrypt Mode (3 keys: k, k , k ) c = DESk(DESk (DESk (m))) 1/31/12 Nikita Borisov — UIUC 20 Was not reported in open literature until 1990 Tracks probabilities of differences inputs matching differences in outputs Chosen ciphertext attack 1/31/12 Nikita Borisov — UIUC 21 Build table of probabilities of inputs and outputs per round ∆mi+1 = mi+1 xor m’i+1 ∆mi+1 = [mi-1 xor f(mi,Ki)] xor [ m’i-1 xor f(m’i, Ki)] ∆mi+1 = ∆mi-1 xor [f(mi,Ki) xor f(m’i, Ki)] Compose probabilities per round 1/31/12 Nikita Borisov — UIUC 22 Revealed several properties Small changes in S-boxes reduces the number of pairs needed The method was known to designer team as early as 1974 Not so useful to break DES But very useful to analyze the security of Feistel Network systems 1/31/12 Nikita Borisov — UIUC 23 Lucifer – IBM precursor to DES Broken in 30 pairs FEAL-N DES with different numbers of iterations FEAL-4 broken in 20 pairs FEAL-8 broken in 10,000 pairs DES with 15 rounds broken in 252 tests DES with 16 rounds broken in 258 tests 1/31/12 Nikita Borisov — UIUC 24 A design for computer system and an associated software that could break any DES-enciphered message in a few days was published in 1998 Several challenges to break DES messages solved using distributed computing National Institute of Standards and Technology (NIST) selected Rijndael as Advanced Encryption Standard (AES), successor to DES Designed to withstand attacks that were successful on DES It can use keys of varying length (128, 196, or 256) 1/31/12 Nikita Borisov — UIUC 25 Clear a replacement for DES was needed Can use Triple-DES –but slow with small blocks US NIST issued call for ciphers in 1997 15 candidates accepted in Jun 98 5 were short-listed in Aug-99 Rijndael was selected as AES in Oct-2000 issued as FIPS PUB 197 standard in Nov-2001 http://csrc.nist.gov/publications/fips/fips197/fips- 197.pdf 1/31/12 Nikita Borisov — UIUC 26 Private key symmetric block cipher 128-bit data, 128/192/256-bit keys Stronger & faster than Triple-DES Active life of 20-30 years (+ archival use) Provide full specification & design details Both C & Java implementations NIST have released all submissions & unclassified analyses 1/31/12 Nikita Borisov — UIUC 27 Initial criteria: security –effort to practically cryptanalyse cost –computational algorithm & implementation characteristics Final criteria general security software & hardware implementation ease implementation attacks flexibility (in en/decrypt, keying, other factors) 1/31/12 Nikita Borisov — UIUC 28 1/31/12 Nikita Borisov — UIUC http://www.moserware.com/2009/09/stick-figure-guide-toadvanced.html 29 Designed by Rijmen-Daemenin Belgium Has 128/192/256 bit keys, 128 bit data An iterative rather than Feistel cipher treats data in 4 groups of 4 bytes 4x4 matrix in column major order operates an entire block in every round Designed to be: resistant against known attacks speed and code compactness on many CPUs Simple design 1/31/12 Nikita Borisov — UIUC 30 Can be efficiently implemented on 8-bit CPU Byte substitution works on bytes using a table of 256 entries Shift rows is simple byte shifting Add round key works on byte XORs Mix columns requires matrix multiply in GF(28) on byte values, can be simplified to use a table lookup Only recently have some cryptoanalysis techniques been successful. Biclique Cryptanalysis of the Full AES ▪ http://research.microsoft.com/enus/projects/cryptanalysis/aesbc.pdf ▪ But not yet a practical concern 1/31/12 Nikita Borisov — UIUC 41 Encipher, decipher multiple bits at once Each block enciphered independently Electronic Code Book Mode (ECB) 1/31/12 Nikita Borisov — UIUC 42 Problem: identical plaintext blocks produce identical ciphertext blocks Example: two database records ▪ MEMBER: HOLLY INCOME $100,000 ▪ MEMBER: HEIDI INCOME $100,000 Encipherment: ▪ ABCQZRME GHQMRSIB CTXUVYSS RMGRPFQN ▪ ABCQZRME ORMPABRZ CTXUVYSS RMGRPFQN 1/31/12 Nikita Borisov — UIUC 43 1/31/12 Nikita Borisov — UIUC 44 Insert information about block’s position into the plaintext block, then encipher Cipher block chaining (CBC): Exclusive-or current plaintext block with previous ciphertext block: ▪ c0 = Ek(m0 I) ▪ ci = Ek(mi ci–1) for i > 0 1/31/12 where I is the initialization vector Nikita Borisov — UIUC 45 init. vector 1/31/12 m1 m2 DES DES … c1 c2 … Nikita Borisov — UIUC … 46 ciphertext init. vector 1/31/12 c1 c2 DES DES m1 m2 Nikita Borisov — UIUC … … … 47 If one block of ciphertext is altered, the error propagates for at most two blocks Initial message 3231343336353837 3231343336353837 3231343336353837 3231343336353837 Received as (underlined 4c should be 4b) ef7c4cb2b4ce6f3b f6266e3a97af0e2c 746ab9a6308f4256 33e60b451b09603d Which decrypts to efca61e19f4836f1 3231333336353837 3231343336353837 3231343336353837 Incorrect bytes underlined Plaintext “heals” after 2 blocks 1/31/12 Nikita Borisov — UIUC 48 Often (try to) implement one-time pad by xor’ing each bit of key with one bit of message Example: m = 00101 k = 10010 c = 10111 But how to generate a good key? 1/31/12 Nikita Borisov — UIUC 49 Period estimated to be 1010 Variable length key 1 to 256 bytes Byte based operations Very efficient Array S stores all possible values from 0 to 255 Each step Systematically pick a value from S: this is the next key stream byte Permute S See Schneier’s Solitaire cipher for a pen and paper analog http://www.schneier.com/solitaire.html 1/31/12 Nikita Borisov — UIUC 50 mi-1 ki-1 1/31/12 mi+1 mi ci-1 E ki- Nikita Borisov — UIUC ci E ci+1 ki+1 51 mi-1 ctri-1 EK ctri ci-1 1/31/12 mi+1d mi EK ci Nikita Borisov — UIUC ctri+1 EK ci+1 52 Additional standard modes for DES/AES Losing Synchronicity is fatal All later decryptions will be garbled OFB needs an initialization vector Counter mode lets you generate a bit in the middle of the stream. Lets you operate on blocks in parallel. RC4 is a well-known stream cipher. Used in WEP and SSL 1/31/12 Nikita Borisov — UIUC 53 Symmetric key ciphers AES and DES Today's workhorse algorithms Cryptanalysis attacks on algorithms Product ciphers Stream ciphers RC4 Block ciphers and cipher modes 1/31/12 Nikita Borisov — UIUC 57